Question: Solve for $x$ : $ 5|x + 1| + 5 = -1|x + 1| + 2 $
Explanation: Add $ {1|x + 1|} $ to both sides: $ \begin{eqnarray} 5|x + 1| + 5 &=& -1|x + 1| + 2 \\ \\ { + 1|x + 1|} && { + 1|x + 1|} \\ \\ 6|x + 1| + 5 &=& 2 \end{eqnarray} $ Subtract ${5}$ from both sides: $ \begin{eqnarray} 6|x + 1| + 5 &=& 2 \\ \\ { - 5} &=& { - 5} \\ \\ 6|x + 1| &=& -3 \end{eqnarray} $ Divide both sides by ${6}$ $ \dfrac{6|x + 1|} {{6}} = \dfrac{-3} {{6}} $ Simplify: $ |x + 1| = -\dfrac{1}{2}$ The absolute value cannot be negative. Therefore, there is no solution.